Perhaps it has been a while since you broke up with girlfriend. Nevertheless, some time has passed and the raw emotions has subsided and now, the two of you can talk again.
How can you start talking again to your ex girlfriend without it being awkward?
Well, if you haven't even established contact with her yet, the best natural way to do this is to just find a simple reason to talk to her. Come up with some things that she is fond of and find out if any of those would be a good enough reason to get back in touch with her. If she is a fan of the band Modest Mouse, you might let her know if they are playing in town sometime soon. Shift to a casual coffee date quickly so that you can see her in person after getting back in touch with her.
This will allow you to really meet her again instead of speaking on the phone or over email.
When you meet your ex girlfriend again in person and start talking, make sure that you act fully relaxed. You don't want to appear awkward or intimidated by her. While you keep a light and fun conversation if possible, don't be scared to talk about serious things if she wants to.
Treat this like any other date. A conversation with your ex girlfriend don't have to be any more tense or awkward than with an old friend or a girl you're dating for the first time.
During your talk to your ex girlfriend, feel free to flirt. Through this way, you can most likely boost the romance and revive those feelings of attraction between the two of you.
Continue to see your ex girlfriend more casually after the first date. Date her like you would a new woman you're meeting. Keep talking to your ex girlfriend and if things appear to be going well after a few dates, ask her if she thinks you two should give your relationship another chance.
By looking for any reason to talk to her, you can begin talking to your ex girlfriend again. This unlocks the channels of communication again between her and you. Just begin talking to her like you would when the two of you were together, by being relaxed and comfortable but not baby-talk or with pet names. Don't be afraid to flirt with her and keep seeing her regularly.
Maintain this for a few weeks and when things feel okay, ask her to give a relationship with you another shot. If things feel fine and they are nice for her, she should be more than happy to say yes to you.